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Linear Algebra true/false explanation.

  1. Mar 5, 2009 #1
    Linear Algebra true/false explanation. :)

    1. The problem statement, all variables and given/known data

    True or False:
    Is it possible to find a pair of two-dimensional subspaces S and T of R3 such that S (upside down U) = {0} ?

    2. Relevant equations



    3. The attempt at a solution

    My understanding: upside down U = intersection, and for S to intersect T, S must have some vectors that are linear combinations of the vectors of T (and vice versa). These combinations have to = 0... and that's all I've got. I've sifted through my notes and the textbook several times, and the only other thing I could come up with that may or may not be useful (I haven't connected the dots yet), is that:
    Def: the vectors v1, v2,...,vn in a vector space V are said to be linearly independent if
    c1v1+c2v2+...+cnvn = 0
    which implies that all the scalars c1...cn must equal zero

    (the answer in the back of the book says that the answer is false, which is why I was looking at linear independence.)
    Thanks!
     
  2. jcsd
  3. Mar 5, 2009 #2

    Mark44

    Staff: Mentor

    Re: Linear Algebra true/false explanation. :)

    Think about the geometry of your problem. S and T are both two-dimensional subspaces of R^3, which means that both (S and T) are planes that contain the origin. Is it possible to have two planes in R^3, both containing the origin, that intersect at no other points?
     
  4. Mar 5, 2009 #3
    Re: Linear Algebra true/false explanation. :)

    No. So does = {0} mean they only contain the origin then?
     
  5. Mar 5, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Linear Algebra true/false explanation. :)

    Yes, {x} means a set that contains only the single member x. Surely you knew that?
     
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